TY  - BOOK
AU  - Beyer,Horst Reinhard
ED  - SpringerLink (Online service)
TI  - Beyond Partial Differential Equations: On Linear and Quasi-Linear Abstract Hyperbolic Evolution Equations 
T2  - Lecture Notes in Mathematics,
SN  - 9783540711292
AV  - QA299.6-433 
U1  - 515 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Global analysis (Mathematics)
KW  - Operator theory
KW  - Differential equations, partial
KW  - Analysis
KW  - Operator Theory
KW  - Partial Differential Equations
N1  - Conventions -- Mathematical Introduction -- Prerequisites -- Strongly Continuous Semigroups -- Examples of Generators of Strongly Continuous Semigroups -- Intertwining Relations, Operator Homomorphisms -- Examples of Constrained Systems -- Kernels, Chains, and Evolution Operators -- The Linear Evolution Equation -- Examples of Linear Evolution Equations -- The Quasi-Linear Evolution Equation -- Examples of Quasi-Linear Evolution Equations
N2  - The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics
UR  - https://doi.org/10.1007/978-3-540-71129-2
ER  -